α-凹壳--凸包的推广
Alpha-Concave Hull, a Generalization of Convex Hull
摘要：
包围壳，如凸包、凹壳、α形等，在各个领域特别是在计算几何中有着广泛的应用。α形和凹壳是凸包的推广。与凸包不同，它们在一组点上构造非凸包围。本文介绍了凸包的另一种推广形式--α-凹包，并与凸包和α形进行了比较。我们表明，α-凹壳也是一个推广的NP完全问题，名为最小面积TSP。我们证明了计算的α凹壳是NP-困难的一组点。
英文摘要：
Bounding hull, such as convex hull, concave hull, alpha shapes etc. has vast applications in different areas especially in computational geometry. Alpha shape and concave hull are generalizations of convex hull. Unlike the convex hull, they construct non-convex enclosure on a set of points. In this paper, we introduce another generalization of convex hull, named alpha-concave hull, and compare this concept with convex hull and alpha shape. We show that the alpha-concave hull is also a generalization of an NP-complete problem named min-area TSP. We prove that computing the alpha-concave hull is NP-hard on a set of points.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
